What do the following two equations represent? $5x+4y = 2$ $5x+4y = 0$
Solution: Putting the first equation in $y = mx + b$ form gives: $5x+4y = 2$ $4y = -5x+2$ $y = -\dfrac{5}{4}x + \dfrac{1}{2}$ Putting the second equation in $y = mx + b$ form gives: $5x+4y = 0$ $4y = -5x$ $y = -\dfrac{5}{4}x + 0$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.